Complex Survey And Design Effect With Rao-Scott Correction And Log-Linear Analysis

Abstract

Collection of data through sample surveys involves a wide range of techniques and procedures. Data is collected with the priority of maximum accuracy of information and with minimum cost and effort. Various sampling techniques are used to achieve the objective of accuracy and low cost. When the data is collected from a complex surveys techniques for the analysis of categorical data (e.g. the chi-squared test for association between pairs of variable) have to be modified from the procedures used when the sample design is assumed to be a simple random sample. When the data is acquired using various sampling techniques in a complex design, there is a sample design effect on whatever analysis is used. Rao-Scott showed the effect of design on the tests of fitness, homogeneity and independence. The Log-linear model is used for analysis of higher dimension categorical data. The modifications of this analysis for complex survey designs were also proposed by Rao-Scott. Simultaneous Test Procedure, another method, to test the homogeneity between multiple categories can also be linked with log-likelihood ratio statistics. The fundamental concepts of data collection are explained with examples. The basic concepts of test procedure along with ways to get log-linear models are discussed leading to the multi-dimension with general log-linear model. The examples following the concepts show the validity in calculation.